Basic Stochastic Calculus

Abstract

Stochastic calculus serves as a fundamental tool throughout this book. This chapter is meant to be a convenient “User’s Guide” on stochastic calculus for use in the subsequent chapters. Specifically, it collects the definitions and results in stochastic calculus scattered around in the literature that are related to stochastic controls. It also unifies terminology and notation (which may differ in different papers/books) that are to be used in later chapters. Proofs of the results presented in this chapter are either given (which is the case when we think that the proof is important in understanding the subsequent material and/or when there is no immediate reference available) or else referred to standard and easily accessible books. Knowledgeable readers may skip this chapter or regard it as a quick reference.